Solve for $x$ : $ 8|x + 10| + 8 = 5|x + 10| + 4 $
Solution: Subtract $ {5|x + 10|} $ from both sides: $ \begin{eqnarray} 8|x + 10| + 8 &=& 5|x + 10| + 4 \\ \\ { - 5|x + 10|} && { - 5|x + 10|} \\ \\ 3|x + 10| + 8 &=& 4 \end{eqnarray} $ Subtract ${8}$ from both sides: $ \begin{eqnarray} 3|x + 10| + 8 &=& 4 \\ \\ { - 8} &=& { - 8} \\ \\ 3|x + 10| &=& -4 \end{eqnarray} $ Divide both sides by ${3}$ $ \dfrac{3|x + 10|} {{3}} = \dfrac{-4} {{3}} $ Simplify: $ |x + 10| = -\dfrac{4}{3}$ The absolute value cannot be negative. Therefore, there is no solution.